I won't reiterate how much of a geek I am (trust me, I am), but when I randomly stumble upon something insanely geekish that is (somewhat) related to ancient Hellas, you can be darn sure I will be blogging about it: in this case several icosahedron in the collection of the Metropolitan Museum of Art, which date back to the Ptolemaic Period (so between 304-30 BC) and were found in Egypt. The symbols on the shapes are part of the coptic aphabet. The repertoire of glyphs is based on the Greek alphabet augmented by letters borrowed from the Egyptian Demotic and is the first alphabetic script used for the Egyptian language. Incidentally, the icosahedron--a polyhedron with twenty faces--is a often used dice in table top roleplaying games, and in modern times it carries numbers. As ancient Hellenic lettering often doubled as numbers themselves, the similarities are striking.The term 'icosahedron' comes from Hellenic 'είκοσι' (eíkosi), meaning 'twenty', and 'εδρα' (hédra), meaning 'seat'. It was a shape well known in ancient Hellas. It is mentioned, for example, in Eukleidēs' 'Elements'. Eukleidēs (Euclid) of Alexandria was a Hellenic mathematician, often referred to as the 'Father of Geometry'. He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His 'Elements' is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. Eukleidēs defines the icosahedron as 'a solid figure contained by twenty equal and equilateral triangles'. In 'Elements' he proposes to 'construct an icosahedron and comprehend it in a sphere, and to prove that the square on the side of the icosahedron is the irrational straight line called minor. After a long list of equations and proves, he eventually concludes that:
"[T]he square on the diameter of the sphere is five times the square on the radius of the circle from which the icosahedron has been described, and that the diameter of the sphere is composed of the side of the hexagon and two of the sides of the decagon inscribed in the same circle." [Book XIII, Proposition 16]
For what the icosahedrons were used is unknown. Personally, I could see them be used as lots, as tools for divination, or even just as a part of a game like we use these shapes today. All of this to say that I recently had a major geek moment over a bunch of carved minerals (the dice are made out of Serpentine), and I need one of these, pronto. I recently found out, by the way, that you can buy a replica for about 16 euro's. For anyone reading this who has me on their Christmas list, this is a not-so-subtle hint.
I use tabletop RPG dice for my divination, though I find the d20 awkward for giving to the letters (I can't easily see which letters are missing from the die). Of the standard set of dice, I use the d4, d8, d20, and d6 for geomancy (these being the Platonic solids of Fire, Air, Water, and Earth, respectively).
ReplyDeleteI use the d12 for my Greek alphabet divination. When I use the d12, I roll the die twice: the first roll determines which half of the alphabet I get a letter from (odd = first set of 12 letters Α-Μ, even = second set of 12 letters Ν-Ω), and the second roll determines which letter within that set. So, let's say I roll a 5 and a 9; the first roll is odd, so I get the ninth letter of the first half of the alphabet, or Ι. Works well for me!